Geometry & Topology

Skeleta of affine hypersurfaces

Helge Ruddat, Nicolò Sibilla, David Treumann, and Eric Zaslow

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Abstract

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n–dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation T of its Newton polytope , we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.

Article information

Source
Geom. Topol., Volume 18, Number 3 (2014), 1343-1395.

Dates
Received: 11 July 2013
Revised: 19 December 2013
Accepted: 17 January 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732797

Digital Object Identifier
doi:10.2140/gt.2014.18.1343

Mathematical Reviews number (MathSciNet)
MR3228454

Zentralblatt MATH identifier
1326.14102

Subjects
Primary: 14J70: Hypersurfaces
Secondary: 14R99: None of the above, but in this section

Keywords
skeleton retraction hypersurface homotopy equivalence affine toric degeneration Kato–Nakayama space log geometry Newton polytope triangulation

Citation

Ruddat, Helge; Sibilla, Nicolò; Treumann, David; Zaslow, Eric. Skeleta of affine hypersurfaces. Geom. Topol. 18 (2014), no. 3, 1343--1395. doi:10.2140/gt.2014.18.1343. https://projecteuclid.org/euclid.gt/1513732797


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